Similarity coefficients play an important role in many application aspects. Recently, a privacy-preserving similarity coefficients protocol for binary data was proposed by Wong and Kim (Computers and Mathematics with Application 2012). In this paper, we show that their protocol is not secure, even in the semi-honest model, since the client can retrieve the input of the server without deviating from the protocol. Also we propose a secure similarity coefficients computation in the presence of malicious adversaries, and prove it using the standard simulation-based security definitions for secure two-party computation. We also discuss several extensions of our protocol for settling other problems. Technical tools in our protocol include zero-knowledge proofs and distributed ElGamal encryption.

Wireless sensor networks (WSNs) are applied widely a variety of areas such as real-time traffic monitoring, measurement of seismic activity, wildlife monitoring and so on. User authentication in WSNs is a critical security issue due to their unattended and hostile deployment in the field. In 2010, Yuan et al. proposed the first biometric-based user authentication scheme for WSNs. However, Yoon et al. pointed out that Yuan et al.\'s scheme is vulnerable to the insider attack, user impersonation attack, GW-node impersonation attack and sensor node impersonate attack. To improve security, Yoon et al.\'s proposed an improved scheme and claimed their scheme could withstand various attacks. Unfortunately, we will show Yoon et al.\'s scheme is vulnerable to the denial-of-service attack (DoS) and the sensor node impersonation attack. To overcome the weaknesses in Yoon et al.\'s scheme, we propose a new biometric-based user authentication scheme for WSNs. The analysis shows our scheme is more suitable for practical applications.

We initiate the study of unique group signature such that signatures of the same message by the same user will always have a large common component (i.e., unique identifier). We present a number of unique group signature schemes under a variety of security models that extend the standard security models of ordinary group signatures (without random oracles). Our work is a beneficial step towards mitigating the well-known group signature paradox, and it also has many other interesting applications and efficiency implications.

The design of secure remote user authentication schemes for mobile applications is still an open and quite challenging problem, though many schemes have been published lately. Recently, Islam and Biswas pointed out that Lin and Hwang et al.\'s password-based authentication scheme is vulnerable to various attacks, and then presented an improved scheme based on elliptic curve cryptography (ECC) to overcome the drawbacks. Based on heuristic security analysis, Islam and Biswas claimed that their scheme is secure and can withstand all related attacks. In this paper, however, we show that Islam and Biswas\'s scheme cannot achieve the claimed security goals and report its flaws: (1) It is vulnerable to offline password guessing attack, stolen verifier attack and denial of service (DoS) attack; (2) It fails to preserve user anonymity. The cryptanalysis demonstrates that the scheme under study is unfit for practical use.

Prefix-preserving encryption (PPE) is an important type of encryption scheme, having a wide range of applications, such as IP addresses anonymization, prefix-matching search, and rang search. There are two issues in PPE schemes, security proof and single key requirement.

Existing security proofs for PPE only reduce the security of a real PPE scheme to that of the ideal PPE object by showing their computational indistinguishability \\cite{Ama07,Xu02}. Such security proof is incomplete since the security of the ideal encryption object is unknown. Also, existing prefix-preserving encryption schemes only consider a single encryption key, which is infeasible for a practical system with multiple users (Implying that all users should have the single encryption key in order to encrypt or decrypt confidential data).

In this paper we develop a novel mechanism to analyze the security of the ideal PPE object. We follow the modern cryptographic approach and create a new security notion IND-PCPA. Then, we show that such weakened security notion is necessary and the ideal PPE object is secure under IND-PCPA.

We also design a new, security-enhanced PPE protocol to support its use in multi-user systems, where no single entity in the system knows the PPE key. The protocol secret shares and distributes the PPE key to a group of key agents and let them ``distributedly encrypt\'\' critical data. We develop a novel distributed PPE algorithm and the corresponding request and response protocols. Experimental results show that the protocol is feasible in practical systems.

Several order preserving encryption (OPE) algorithms have been developed in the literature to support search on encrypted data. However, existing OPE schemes only consider a single encryption key, which is infeasible for a practical system with multiple users (implying that all users should have the single encryption key in order to encrypt or decrypt confidential data). In this paper, we develop the first protocols, DOPE and OE-DOPE, to support the use of OPE in multi-user systems. First, we introduce a group of key agents into the system and invent the DOPE protocol to enable \"distributed encryption\" to assure that the OPE encryption key is not known by any entity in the system. However, in DOPE, if a key agent is compromised, the share of the secret data that is sent to this key agent is compromised. To solve the problem, we developed a novel oblivious encryption (OE) protocol based on the oblivious transfer concept to deliver and encrypt the shares obliviously. Then, we integrate it with DOPE to obtain the OE-DOPE protocol. Security of OE-DOPE is further enhanced with additional techniques. Both DOPE and OE-DOPE can be used with any existing OPE algorithms while retaining all the advantages of OPE without requiring the users to share the single encryption key, making the OPE approach feasible in practical systems.

The homomorphic encryption problem has been an open one for three decades. Recently, Gentry has proposed a full solution. Subsequent works have made improvements on it. However, the time complexities of these algorithms are still too high for practical use. For example, Gentry\'s homomorphic encryption scheme takes more than 900 seconds to add two 32 bit numbers, and more than 67000 seconds to multiply them. In this paper, we develop a non-circuit based symmetric-key homomorphic encryption scheme. It is proven that the security of our encryption scheme is equivalent to the large integer factorization problem, and it can withstand an attack with up to m ln⁡poly⁡(λ) chosen plaintexts for any predetermined m, where λ is the security parameter. Multiplication, encryption, and decryption are almost linear in mλ, and addition is linear in mλ. Performance analyses show that our algorithm runs multiplication in 108 milliseconds and addition in a tenth of a millisecond for λ=1024 and m=16.

We further consider practical multiple-user data-centric applications. Existing homomorphic encryption schemes only consider one master key. To allow multiple users to retrieve data from a server, all users need to have the same key. In this paper, we propose to transform the master encryption key into different user keys and develop a protocol to support correct and secure communication between the users and the server using different user keys. In order to prevent collusion between some user and the server to derive the master key, one or more key agents can be added to mediate the interaction.